The correct answer is $\boxed{\text{A. 3 : 2}}$.
When a partner dies, the surviving partners take the deceased partner’s share in the ratio of their original profit-sharing interests. In this case, X and Y’s original profit-sharing interests were $\frac{1}{2}$ and $\frac{1}{3}$, respectively. Therefore, X’s new profit-sharing interest is $\frac{1}{2} + \frac{1}{6} = \frac{3}{6}$, and Y’s new profit-sharing interest is $\frac{1}{3} + \frac{1}{6} = \frac{2}{6}$. Therefore, X and Y’s new profit-sharing ratio is $\frac{3}{6} : \frac{2}{6} = 3 : 2$.
Option B is incorrect because it is the original profit-sharing ratio of X and Y. Option C is incorrect because it is the original profit-sharing ratio of X and Z. Option D is incorrect because it is not a valid profit-sharing ratio.